Constant function

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Definition

Let $A$ and $B$ be sets and $f:A\rightarrow B$ be any function between them. We call $f$ a "constant function" if:

• $\exists b\in B\forall a\in A[f(a)=b]$
  • In words: every $a\in A$ is sent to the same $b\in B$ by $f$.

We may write $f$ as:

• $f:A\rightarrow B$ given by $f:a\mapsto b$

Terminology

• Constant map and constant mapping are obviously also used.
• Trivial map might be used to describe a constant map (and I am sure I have seen it) but this is rare and ill-advised.

References

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This terminology is... A-level, possibly earlier, and doesn't really need a page. So finding references will be difficult anyway as who would bother to write it!